You can install your own custom php version of PHP and include libraries/modules/extensions, including zip libraries, that are not available in the default installation of PHP provided by Dreamhost.
The link provided above has detailed instructions, but you are likely to need to be fairly proficient in the use of the *nix shell and have good knowledge of the PHP installation process to be successful adding your own libraries to your install.
Everything you need to know is available in that wiki article or by searching the web. DreamHost support will not help you with this, but if you have specific problems or have a question, there are many users in these forums that might be able/willing to help you.
–rlparker